Re: Mathematics as Images

Dear W3C Friends,

I think that I should patiently explain the problem of representing
mathematical notation as an image rather than text. Also, why this relates
to SC.1.410.



Issues with  Notation as Image.

The attached files give two images of a text page from the  Vital Source
bookshelf. Image_1 is the print part of a screen capture for page xx from
Projective Geometry by yy. The second image is of the same page with a
vertical midline and a square enclosing an image of mathematics text. As is
plane this image cannot enlarge to 400% without running off the page. This
is because it occupies more than half of the page width at 100%.

Now as stated 1.4.10 would allow this because the notation in the box is an
image and exempted from reflow. The problem is that authors put formulas in
a format so that they appear on one screen so that readers understand
relations between objects at a single glance.

In this example the author wants the reader to appreciate the equality of
the function beta applied to four cyclic permutations of the parameters. It
is clear that the author intends for readers to equate all for expressions
in the same statement. Thus, to meet the author’s intension this formula
should  appear on one screen when presented. This is not satisfied by an
image that cannot fit on a screen. If, however, the image was split into
four pieces and allowed to reflow the entire sequence would appear on one
screen, and the visually impaired reader could have the learning experience
intended by the author. For those of you that do not read at 400%, you
should note that more than for lines fit on a page at 400% of say 12 point.



Notation is Text

The images of mathematics that we read  in books and web pages are
constructed from markup languages like LaTeX or MathML. These expressions
consist of markup element symbols and characters from a few special
alphabets. All the characters are represented as single characters in
Unicode. For example, the integral symbol is U+222B. As such they can be
enlarged as characters, converted to braille, and read out loud. They can
be parsed like  any other computer language.

Also, mathematical notation can be spoken. This is important. The main
contribution of algebra was to integrate mathematical computations into
written language. Before algebra people used to write out all their
calculations in language. Galileo wrote  out some of his theories as plays.

Images cannot be parsed into language. Once a markup language is converted
to an image its linguistic properties are lost to media players. Even SVG
can only give geometric descriptions of character curves. It does not hold  the
semantic information of characters.

The fact that notation is text means that its linguistic structure can be
exploited to identify break points in lines when we need to convert
paragraphs into lines (reflow).



I do hope this begins to explain the problems with using images to
represent mathematics and the need for reflow.



Most of you do not know  what it is like to read mathematics with low
vision. It is hard to imagine. I know enlargement tricks most of you have
never imagined. I need to. I use browser zoom, screen magnifiers, CSS,
Word, LaTeX, Jupyter and even some tricks with PDF.



Best, Wayne





On Thu, Jul 20, 2023 at 3:52 PM Patrick H. Lauke <redux@splintered.co.uk>
wrote:

> On 20/07/2023 23:35, Steve Green wrote:
> [...]
>
> > Based on those definitions, I would say there is a very strong case that
> formulae are text and that images of formulae violate SC 1.4.5 Images of
> Text.
>
> Note though the start of 1.4.5 "If the technologies being used can
> achieve the visual presentation". As said, while MathML has been getting
> better, with support coming directly into browsers (rather than
> requiring some plugin solution), I'm not sure it's as pervasively
> supported yet to be able to fail formulae presented as images.
>
> Also - and I'll admit I'm not too hot on MathML ... are there actually
> defined rules for how MathML itself is supposed to reflow, at a
> technical level?
>
> P
> --
> Patrick H. Lauke
>
> https://www.splintered.co.uk/ | https://github.com/patrickhlauke
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>
>